Finite Group Databasebeta

← #7643146

Subgroups — #7643146

Order 512.

6766 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C2×#3522C211yesmaximal, characteristic, complemented
3#39747C211yesmaximal, characteristic, complemented
4#39746C211yesmaximal, characteristic, complemented
5#39741C212yesmaximal, complemented
6#39619C211yesmaximal, characteristic, complemented
7#39618C211yesmaximal, characteristic, complemented
8#39613C212yesmaximal, complemented
9#39174C211yesmaximal, characteristic, complemented
10#39173C211yesmaximal, characteristic, complemented
11#39172C211yesmaximal, characteristic, complemented
12#39171C211yesmaximal, characteristic, complemented
13#39166C214yesmaximal, complemented
14#39164C212yesmaximal, complemented
15#39163C212yesmaximal, complemented
16#38950C214yesmaximal, complemented
17#38087C218yesmaximal, complemented
18#37193C218yesmaximal, complemented
19#36639C211yesmaximal, characteristic, complemented
20#36631C211yesmaximal, characteristic, complemented
21#35675C214yesmaximal, complemented
22#35625C214yesmaximal, complemented
23#35326C212yesmaximal, complemented
24#35303C212yesmaximal, complemented
25#35241C211yesmaximal, characteristic, complemented
26#35238C211yesmaximal, characteristic, complemented
27#35180C212yesmaximal, complemented
28#35103C212yesmaximal, complemented
29C2×#2295C211yesmaximal, characteristic, complemented
30#3523—216no—
31#3522—216no—
32C2×#559C2211yescharacteristic
33C2×#559C2212yes—
34C2×Q82C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#557C2211yescharacteristic
37C2×#557C2212yes—
38C2×#556C2211yescharacteristic
39C2×#556C2212yes—
40C2×#554C2211yescharacteristic
41C2×#554C2212yes—
42C2×#552C2212yes—
43C2×#552C2214yes—
44C2×#550C2211yescharacteristic
45C2×D4×Q8C2211yescharacteristic
46C2×D4×Q8C2212yes—
47C2×#548C2212yes—
48C2×#547C2212yes—
49C2×#547C2214yes—
50C2×#542C2214yes—
51C2×#542C2212yes—
52C2×#541C2212yes—
53C2×#541C2214yes—
54C2×#533C2211yescharacteristic
55C2×#533C2212yes—
56C2×#532C2211yescharacteristic
57C2×#532C2212yes—
58C2×#529C2211yescharacteristic
59C2×#529C2211yescharacteristic
60C2×#529C2212yes—
61C2×#529C2212yes—
62C2×#520C2212yes—
63C2×#519C2212yes—
64C22×C4×Q8C2211yescharacteristic
65#2862C2211yescharacteristic
66#2862C2211yescharacteristic
67#2861C2211yescharacteristic
68#2861C2211yescharacteristic
69#2861C2214yes—
70#2860C2214yes—
71#2859C2211yescharacteristic
72#2858C2211yescharacteristic
73#2858C2211yescharacteristic
74#2858C2211yescharacteristic
75#2857C2211yescharacteristic
76#2857C2212yes—
77#2856C2211yescharacteristic
78#2856C2212yes—
79#2854C2214yes—
80#2850C2211yescharacteristic
81#2850C2211yescharacteristic
82#2850C2212yes—
83#2850C2214yes—
84#2850C2212yes—
85#2850C2212yes—
86#2850C2212yes—
87#2731C2218yes—
88#2730C2218yes—
89#2729C2218yes—
90#2728C2218yes—
91#2716C2218yes—
92#2714C2218yes—
93#2713C2218yes—
94#2711C2218yes—
95#2707C2218yes—
96#2705C2218yes—
97#2704C2218yes—
98#2702C2218yes—
99#2696C2218yes—
100#2694C2218yes—
101#2692C2218yes—
102#2690C2218yes—
103#2664C2214yes—
104#2662C2214yes—
105#2660C2212yes—
106#2660C2212yes—
107#2658C2212yes—
108#2657C2212yes—
109#2642C2212yes—
110#2641C2212yes—
111#2640C2212yes—
112#2640C2212yes—
113#2639C2218yes—
114#2618C2218yes—
115#2611C2218yes—
116#2610C2218yes—
117#2604C2218yes—
118#2603C2218yes—
119#2601C2218yes—
120#2601C2218yes—
121#2592C2218yes—
122#2568C2211yescharacteristic
123#2568C2212yes—
124#2568C2212yes—
125#2567C2211yescharacteristic
126#2566C2212yes—
127#2566C2212yes—
128#2566C2212yes—
129#2565C2212yes—
130#2565C2212yes—
131#2565C2212yes—
132#2564C2218yes—
133#2563C2212yes—
134#2563C2211yescharacteristic
135#2563C2212yes—
136#2562C2218yes—
137#2548C2212yes—
138#2548C2211yescharacteristic
139#2548C2212yes—
140#2547C2212yes—
141#2547C2211yescharacteristic
142#2547C2212yes—
143#2546C2211yescharacteristic
144#2545C2212yes—
145#2545C2212yes—
146#2545C2212yes—
147#2544C2212yes—
148#2544C2212yes—
149#2544C2212yes—
150#2543C2218yes—
151#2542C2211yescharacteristic
152#2541C2211yescharacteristic
153#2498C2218yes—
154#2498C2214yes—
155#2481C2218yes—
156#2477C2218yes—
157#2473C2218yes—
158#2471C2218yes—
159#2467C2218yes—
160#2465C2218yes—
161#2460C2218yes—
162#2458C2218yes—
163#2454C2214yes—
164#2451C2214yes—
165#2448C2214yes—
166#2446C2214yes—
167#2442C2214yes—
168#2439C2214yes—
169#2436C2214yes—
170#2432C2214yes—
171#2430C2218yes—
172#2430C2214yes—
173#2427C2214yes—
174#2426C2214yes—
175#2421C2214yes—
176#2421C2214yes—
177#2417C2214yes—
178#2417C2214yes—
179#2416C2214yes—
180#2414C2214yes—
181#2409C2214yes—
182#2407C2214yes—
183#2328C2212yes—
184#2328C2212yes—
185#2327C2212yes—
186#2327C2212yes—
187#2326C2212yes—
188#2326C2212yes—
189#2326C2212yes—
190#2326C2212yes—
191#2325C2218yes—
192#2324C2214yes—
193#2323C2214yes—
194#2311C2218yes—
195C4×C4⋊Q8C2211yescharacteristic
196C4×#127C2211yescharacteristic
197C4×#124C2211yescharacteristic
198C4×#124C2211yescharacteristic
199C4×#124C2214yes—
200C4×#124C2212yes—
201C4×#124C2212yes—
202C4×#121C2214yes—
203#2297C2214yes—
204#2295C2211yescharacteristic
205#2295C2211yescharacteristic
206#2295C2212yes—
207#2295C2212yes—
208#2295C2211yescharacteristic
209#2295C2211yescharacteristic
210#2295C2214yes—
211#2295C2212yes—
212#2295C2212yes—
213C2×#391C2212yes—
214#2293C2214yes—
215C2×#389C2212yes—
216C2×#387C2214yes—
217C2×C4×C4⋊C4C2212yes—
218C2×C4×C4⋊C4C2211yescharacteristic
219C2×#376C2212yes—
220C2×C43C2211yescharacteristic
221C22×#41C2314yes—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C23×Q8C2312yes—
225C23×Q8C2311yescharacteristic
226#559—28no—
227#559—216no—
228Q82—28no—
229#557—28no—
230#557—28no—
231#557—216no—
232#556—28no—
233#556—216no—
234#554—28no—
235#554—216no—
236#552—216no—
237#552—232no—
238#550—28no—
239D4×Q8—216no—
240D4×Q8—28no—
241#548—216no—
242#547—216no—
243#547—232no—
244#542—216no—
245#542—232no—
246#541—216no—
247#541—232no—
248#533—28no—
249#533—216no—
250#532—28no—
251#532—216no—
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2312yes—
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2314yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2314yes—
263C2×C4⋊Q8C2312yes—
264C2×#127C2311yescharacteristic
265C2×#127C2311yescharacteristic
266C2×#127C2312yes—
267C2×#127C2312yes—
268#529—28no—
269#529—216no—
270#529—28no—
271#529—216no—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2312yes—
275C2×#126C2312yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2314yes—
280C2×#125C2311yescharacteristic
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2311yescharacteristic
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2312yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2311yescharacteristic
293C2×#124C2311yescharacteristic
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2314yes—
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#124C2314yes—
302C2×#124C2311yescharacteristic
303C2×#124C2312yes—
304C2×#124C2311yescharacteristic
305C2×#123C2312yes—
306C2×#123C2312yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2311yescharacteristic
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2311yescharacteristic
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×#121C2311yescharacteristic
328C2×#121C2312yes—
329C2×#121C2312yes—
330C2×#121C2311yescharacteristic
331C2×#121C2314yes—
332C2×#121C2312yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2318yes—
336C2×#121C2314yes—
337#520—216no—
338#519—216no—
339C2×C4×Q8D4116yescomplemented
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2314yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2314yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2312yes—
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2314yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2314yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2314yes—
375C2×#117C2314yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2314yes—
379C2×#117C2314yes—
380C2×#117C2312yes—
381C2×#117C2314yes—
382C2×#117C2312yes—
383C22×C4⋊C4C2312yes—
384C22×C4⋊C4C2314yes—
385C22×C4⋊C4C2314yes—
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2311yescharacteristic
389C22×C42C2311yescharacteristic
390C22×C42C2311yescharacteristic
391C22×C42C2312yes—
392C22×C42C2312yes—
393C22×C42C2312yes—
394C22×C42C2311yescharacteristic
395C22×C42C2312yes—
396#400C2318yes—
397#400C2318yes—
398#400C2318yes—
399#400C2314yes—
400#400C2318yes—
401#399C2318yes—
402#399C2318yes—
403#399C2314yes—
404#398C2318yes—
405#398C2318yes—
406#398C2318yes—
407#398C2318yes—
408#398C2318yes—
409#398C2314yes—
410#397C2318yes—
411#397C2318yes—
412#397C2318yes—
413#397C2318yes—
414#397C2314yes—
415#396C2318yes—
416#396C2318yes—
417#396C2318yes—
418#396C2318yes—
419#396C2318yes—
420#396C2318yes—
421#395C2318yes—
422#395C2314yes—
423#395C2318yes—
424#394C2318yes—
425#394C2318yes—
426#394C2318yes—
427#394C2318yes—
428#394C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2314yes—
432#393C2318yes—
433#393C2318yes—
434#393C2314yes—
435#393C2318yes—
436#393C2318yes—
437#392C2318yes—
438#392C2318yes—
439#392C2314yes—
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2318yes—
447#391C2318yes—
448#391C2312yes—
449#391C2314yes—
450#391C2311yescharacteristic
451#391C2312yes—
452#391C2311yescharacteristic
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#390C2311yescharacteristic
463#390C2311yescharacteristic
464#390C2314yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2318yes—
471#390C2318yes—
472#390C2318yes—
473#390C2314yes—
474#390C2311yescharacteristic
475#390C2312yes—
476#390C2311yescharacteristic
477#390C2314yes—
478#390C2314yes—
479#390C2314yes—
480#390C2314yes—
481#390C2314yes—
482#390C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2318yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#388C2314yes—
497#388C2318yes—
498#388C2318yes—
499#388C2318yes—
500#388C2318yes—
501#388C2318yes—
502#388C2318yes—
503#388C2318yes—
504#388C2318yes—
505#388C2318yes—
506#388C2318yes—
507#388C2314yes—
508#388C2318yes—
509#388C2318yes—
510#388C2318yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#387C2318yes—
518#387C2318yes—
519#387C2318yes—
520#387C2318yes—
521#387C2318yes—
522#387C2318yes—
523#387C2318yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#386C2318yes—
533#386C2318yes—
534#386C2314yes—
535#386C2318yes—
536#386C2318yes—
537#386C2318yes—
538#386C2314yes—
539#386C2318yes—
540#386C2318yes—
541#386C2318yes—
542#386C2318yes—
543#386C2318yes—
544#386C2318yes—
545#385C2318yes—
546#385C2318yes—
547#385C2318yes—
548#385C2318yes—
549#385C2318yes—
550#385C2318yes—
551#385C2318yes—
552#384C2311yescharacteristic
553#384C2311yescharacteristic
554#384C2312yes—
555#384C2312yes—
556#382C2312yes—
557#382C2311yescharacteristic
558#382C2312yes—
559#382C2312yes—
560#382C2311yescharacteristic
561#382C2312yes—
562#382C2314yes—
563#380C2318yes—
564#380C2318yes—
565#380C2318yes—
566#380C2318yes—
567#380C2314yes—
568#380C2314yes—
569#380C2318yes—
570#380C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2311yescharacteristic
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2311yescharacteristic
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2312yes—
583C4×C22⋊C4C2314yes—
584C4×C22⋊C4C2314yes—
585C4×C22⋊C4C2318yes—
586C4×C22⋊C4C2318yes—
587#376C2312yes—
588#376C2312yes—
589#376C2312yes—
590#376C2312yes—
591#376C2314yes—
592#376C2314yes—
593C2×#95C2314yes—
594C2×#95C2314yes—
595C2×#95C2314yes—
596C2×#95C2312yes—
597C43C2311yescharacteristic
598C43C2311yescharacteristic
599C43C2311yescharacteristic
600C43C2312yes—
601C43C2311yescharacteristic
602C43C2312yes—
603C2×#41—28no—
604C2×#41—216no—
605C2×#41—28no—
606C2×#41—48no—
607C2×#41—416no—
608C2×#41—48no—
609C22×Q8—28no—
610C22×Q8—44no—
611C22×Q8—48no—
612C22×Q8C2×D418yes—
613C22×Q8C2411yescharacteristic
614C22×Q8C2412yes—
615C22×Q8C2411yescharacteristic
616C22×Q8C2412yes—
617C22×Q8C2411yescharacteristic
618C22×Q8C2411yescharacteristic
619C22×Q8C2414yes—
620C22×Q8C2412yes—
621C22×Q8C2414yes—
622C22×Q8C2412yes—
623C22×D4C2412yes—
624C22×D4C2411yescharacteristic
625C22×D4C2412yes—
626C22×D4C2411yescharacteristic
627C22×D4C2412yes—
628C22×D4C2414yes—
629C22×D4C2412yes—
630C22×D4C2414yes—
631C22×D4C2414yes—
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2418yes—
635C23×C4C2412yes—
636C23×C4C2412yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2411yescharacteristic
640C23×C4C2411yescharacteristic
641C23×C4C2411yescharacteristic
642C23×C4C2414yes—
643C23×C4C2412yes—
644C23×C4C2414yes—
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2414yes—
649C23×C4C2412yes—
650C4⋊Q8—28no—
651C4⋊Q8—216no—
652C4⋊Q8—28no—
653C4⋊Q8—216no—
654C4⋊Q8—24no—
655C4⋊Q8—28no—
656C4⋊Q8—28no—
657C4⋊Q8—24no—
658C4⋊Q8—28no—
659C4⋊Q8—24no—
660C4⋊Q8—24no—
661C4⋊Q8—44no—
662#127—24no—
663#127—28no—
664#127—24no—
665#127—44no—
666#126—216no—
667#126—216no—
668#126—216no—
669#126—216no—
670#126—28no—
671#126—216no—
672#126—28no—
673#125—216no—
674#125—216no—
675#125—216no—
676#125—28no—
677#125—216no—
678#125—28no—
679#125—24no—
680#125—24no—
681#125—28no—
682#125—216no—
683#125—28no—
684#124—28no—
685#124—216no—
686#124—24no—
687#124—28no—
688#124—28no—
689#124—24no—
690#124—216no—
691#124—28no—
692#124—28no—
693#124—48no—
694#124—42no—
695#124—44no—
696#124—42no—
697#124—44no—
698#124—44no—
699#123—28no—
700#123—216no—
701#123—28no—
702#123—216no—
703#123—216no—
704#123—216no—
705#123—216no—
706C22⋊Q8—28no—
707C22⋊Q8—216no—
708C22⋊Q8—28no—
709C22⋊Q8—216no—
710C22⋊Q8—24no—
711C22⋊Q8—24no—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—216no—
715C22⋊Q8—28no—
716C22⋊Q8—216no—
717C22⋊Q8—216no—
718C22⋊Q8—216no—
719C22⋊Q8—216no—
720C22⋊Q8—48no—
721#121—24no—
722#121—24no—
723#121—28no—
724#121—28no—
725#121—216no—
726#121—28no—
727#121—216no—
728#121—48no—
729#121—48no—
730#121—416no—
731C4×Q8—28no—
732C4×Q8—28no—
733C4×Q8—28no—
734C4×Q8—216no—
735C4×Q8—28no—
736C4×Q8—216no—
737C4×Q8—28no—
738C4×Q8—24no—
739C4×Q8—24no—
740C4×Q8—28no—
741C4×Q8—28no—
742C4×Q8—28no—
743C4×Q8—28no—
744C4×Q8C2×D418yes—
745C4×Q8C2×D418yes—
746C4×Q8C2×D4116yes—
747C4×Q8C2×D418yes—
748C4×Q8C2×D418yes—
749C4×Q8C2×D4116yes—
750C4×D4—28no—
751C4×D4—216no—
752C4×D4—28no—
753C4×D4—216no—
754C4×D4—28no—
755C4×D4—216no—
756C4×D4—28no—
757C4×D4—216no—
758C4×D4—28no—
759C4×D4—24no—
760C4×D4—24no—
761C4×D4—28no—
762C4×D4—28no—
763C4×D4—28no—
764C4×D4—28no—
765C4×D4—48no—
766#117—216no—
767#117—28no—
768#117—28no—
769#117—216no—
770#117—28no—
771#117—216no—
772#117—28no—
773#117—216no—
774C2×C4⋊C4—28no—
775C2×C4⋊C4—216no—
776C2×C4⋊C4—44no—
777C2×C4⋊C4—48no—
778C2×C4⋊C4C2×D418yes—
779C2×C4⋊C4C2×D4116yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2418yes—
823C2×C4⋊C4C2418yes—
824C2×C4⋊C4C2418yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2418yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2418yes—
859C2×C22⋊C4C2418yes—
860C2×C22⋊C4C2418yes—
861C2×C22⋊C4C2418yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2418yes—
864C2×C22⋊C4C2418yes—
865C2×C22⋊C4C2418yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2418yes—
868C2×C22⋊C4C2418yes—
869C2×C42—24no—
870C2×C42—44no—
871C2×C42—42no—
872C2×C42—44no—
873C2×C42—44no—
874C2×C42C2×D418yes—
875C2×C42C2×D4116yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2412yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2411yescharacteristic
886C2×C42C2411yescharacteristic
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2411yescharacteristic
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2418yes—
925#95C2418yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2418yes—
930#95C2418yes—
931#95C2414yes—
932#95C2414yes—
933#95C2418yes—
934#95C2418yes—
935#95C2418yes—
936#95C2418yes—
937#95C2418yes—
938#95C2418yes—
939C24C2512yes—
940C24C2514yes—
941C24C2512yes—
942C24C2511yescharacteristic
943#41—432no—
944#41—816no—
945#41—832no—
946C2×Q8—22no—
947C2×Q8—24no—
948C2×Q8—22no—
949C2×Q8—28no—
950C2×Q8—24no—
951C2×Q8—28no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—22no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—28no—
959C2×Q8—22no—
960C2×Q8—24no—
961C2×Q8—22no—
962C2×Q8—44no—
963C2×Q8—48no—
964C2×Q8—44no—
965C2×Q8—48no—
966C2×Q8—416no—
967C2×Q8—432no—
968C2×Q8C22×D414yes—
969C2×Q8C22×D414yes—
970C2×Q8C22×D418yes—
971C2×D4—24no—
972C2×D4—24no—
973C2×D4—28no—
974C2×D4—28no—
975C2×D4—216no—
976C2×D4—28no—
977C2×D4—22no—
978C2×D4—24no—
979C2×D4—22no—
980C2×D4—28no—
981C2×D4—24no—
982C2×D4—28no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—22no—
986C2×D4—22no—
987C2×D4—28no—
988C2×D4—28no—
989C2×D4—22no—
990C2×D4—24no—
991C2×D4—22no—
992C2×D4—48no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—48no—
997C2×D4—48no—
998C2×D4—48no—
999C2×D4—48no—
1000C22×C4—24no—
1001C22×C4—28no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—28no—
1008C22×C4—28no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—28no—
1014C22×C4—28no—
1015C22×C4—28no—
1016C22×C4—28no—
1017C22×C4—28no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—44no—
1022C22×C4—48no—
1023C22×C4—48no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—48no—
1027C22×C4—48no—
1028C22×C4—48no—
1029C22×C4C22×D414yes—
1030C22×C4C22×D414yes—
1031C22×C4C22×D418yes—
1032C22×C4C22×D414yes—
1033C22×C4C22×D418yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2512yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C4⋊C4—24no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—28no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—24no—
1077C4⋊C4—22no—
1078C4⋊C4—24no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—22no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—48no—
1102C4⋊C4—48no—
1103C4⋊C4—48no—
1104C4⋊C4C22×D414yes—
1105C4⋊C4C22×D418yes—
1106C4⋊C4C22×D414yes—
1107C4⋊C4C22×D418yes—
1108C4⋊C4C22×D418yes—
1109C4⋊C4C22×D418yes—
1110C4⋊C4C22×D418yes—
1111C22⋊C4—24no—
1112C22⋊C4—28no—
1113C22⋊C4—24no—
1114C22⋊C4—24no—
1115C22⋊C4—24no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—24no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—24no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—24no—
1128C22⋊C4—28no—
1129C22⋊C4—24no—
1130C22⋊C4—28no—
1131C22⋊C4—24no—
1132C22⋊C4—216no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—48no—
1138C22⋊C4—48no—
1139C22⋊C4—48no—
1140C22⋊C4—48no—
1141C22⋊C4—44no—
1142C22⋊C4—48no—
1143C22⋊C4—48no—
1144C22⋊C4—48no—
1145C22⋊C4—44no—
1146C22⋊C4—48no—
1147C22⋊C4—48no—
1148C42—28no—
1149C42—28no—
1150C42—28no—
1151C42—28no—
1152C42—24no—
1153C42—28no—
1154C42—24no—
1155C42—24no—
1156C42—22no—
1157C42—24no—
1158C42—24no—
1159C42—22no—
1160C42—22no—
1161C42—24no—
1162C42—24no—
1163C42—42no—
1164C42—42no—
1165C42—44no—
1166C42—42no—
1167C42—42no—
1168C42—42no—
1169C42—42no—
1170C42—42no—
1171C42C22×D414yes—
1172C42C22×D418yes—
1173C42C22×D418yes—
1174C42C22×D418yes—
1175C42C22×D414yes—
1176C42C22×D414yes—
1177C42C22×D418yes—
1178C42C22×D414yes—
1179C422−1+414yes—
1180C23—21no—
1181C23—21no—
1182C23—22no—
1183C23—22no—
1184C23—24no—
1185C23—22no—
1186C23—24no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—24no—
1191C23—24no—
1192C23—28no—
1193C23—24no—
1194C23—22no—
1195C23—24no—
1196C23—28no—
1197C23—24no—
1198C23C23×D412yes—
1199C23#58514yes—
1200C23C2611yescharacteristic
1201Q8—28no—
1202Q8—28no—
1203Q8—48no—
1204Q8—416no—
1205Q8—48no—
1206Q8—44no—
1207Q8—48no—
1208Q8—44no—
1209Q8—84no—
1210Q8—88no—
1211D4—416no—
1212D4—48no—
1213D4—416no—
1214D4—48no—
1215D4—48no—
1216D4—44no—
1217D4—48no—
1218D4—44no—
1219D4—88no—
1220D4—84no—
1221D4—88no—
1222D4—168no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—28no—
1235C2×C4—216no—
1236C2×C4—28no—
1237C2×C4—28no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—28no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—28no—
1273C2×C4—24no—
1274C2×C4—48no—
1275C2×C4—48no—
1276C2×C4—416no—
1277C2×C4—416no—
1278C2×C4—48no—
1279C2×C4—48no—
1280C2×C4—48no—
1281C2×C4—88no—
1282C2×C4—88no—
1283C2×C4—88no—
1284C2×C4—88no—
1285C2×C4C23×D412yes—
1286C2×C4C23×D414yes—
1287C2×C4C23×D414yes—
1288C2×C4C23×D414yes—
1289C2×C4C23×D412yes—
1290C2×C4C23×D412yes—
1291C2×C4C23×D414yes—
1292C2×C4C23×D412yes—
1293C2×C4C23×D412yes—
1294C2×C4C23×D412yes—
1295C2×C4C2×2−1+414yes—
1296C2×C4C2×2−1+412yes—
1297C2×C4#58514yes—
1298C2×C4#58512yes—
1299C22—22no—
1300C22—24no—
1301C22—24no—
1302C22—22no—
1303C22—42no—
1304C22—44no—
1305C22—42no—
1306C22—44no—
1307C22—42no—
1308C22—42no—
1309C22—44no—
1310C22—48no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—48no—
1315C22—42no—
1316C22—44no—
1317C22—42no—
1318C22#350014yes—
1319C22C24×D411yescharacteristic
1320C22C22×2−1+411yescharacteristic
1321C22C2×#58511yescharacteristic
1322C22C2×#58512yes—
1323C22C2×#58512yes—
1324C4—22no—
1325C4—22no—
1326C4—24no—
1327C4—22no—
1328C4—24no—
1329C4—24no—
1330C4—22no—
1331C4—24no—
1332C4—24no—
1333C4—42no—
1334C4—44no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4—44no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C4#344914yes—
1348C4#349714yes—
1349C2—24no—
1350C2—84no—
1351C2—82no—
1352C2—82no—
1353C2C2×#344911yescharacteristic
1354C2C2×#349711yescharacteristic
1355C2C2×#350011yescharacteristic
1356C2#6282712yes—
1357C2#6283112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3523C2semidirect
2. C2×#3522C2semidirect
3. #39747C2semidirect
4. #39746C2semidirect
5. #39741C2semidirect
6. #39619C2semidirect
7. #39618C2semidirect
8. #39613C2semidirect
9. #39174C2semidirect
10. #39173C2semidirect
11. #39172C2semidirect
12. #39171C2semidirect
13. #39166C2semidirect
14. #39164C2semidirect
15. #39163C2semidirect
16. #38950C2semidirect
17. #38087C2semidirect
18. #37193C2semidirect
19. #36639C2semidirect
20. #36631C2semidirect
21. #35675C2semidirect
22. #35625C2semidirect
23. #35326C2semidirect
24. #35303C2semidirect
25. #35241C2semidirect
26. #35238C2semidirect
27. #35180C2semidirect
28. #35103C2semidirect
29. C2×#2295C2semidirect
339. C2×C4×Q8D4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#35232
C2×#35222
#397472
#397462
#397412
#396192
#396182
#396132
#391742
#391732
#391722
#391712
#391662
#391642
#391632
#389502
#380872
#371932
#366392
#366312
#356752
#356252
#353262
#353032
#352412
#352382
#351802
#351032
C2×#22952